Wave patterns within the generalized convection-reaction-diffusion equation

A set of travelling wave solutions to a hyperbolic generalization of the convection-reaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of the compactly supported soloutions, shock fronts, soliton-like solutions and peakons

💡 Research Summary

The paper investigates travelling‑wave (TW) solutions of a hyperbolic generalisation of the convection‑reaction‑diffusion equation, often called the Generalised Burgers‑Reaction‑Diffusion Equation (GBE). The governing PDE is
α uₜₜ + uₜ + u uₓ − κ ( uⁿ uₓ )ₓ = ( u − U₁ ) φ(u),
where α≥0 accounts for memory (inertial) effects, κ>0 and n>0 describe a nonlinear diffusion term, U₁>0 is a reaction threshold, and φ(u) is taken as (u−U₀)ᵐ ψ(u) with 0≤U₀<U₁, m≥0 and ψ(u) non‑changing sign on